A New Monotone Quantity along the Inverse Mean Curvature Flow in ${\mathbb{R}}^n$

Abstract

We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in ${\mathbb{R}}^n$. As an application, we derive a sharp geometric inequality for mean convex, star-shaped hypersurfaces which relates the volume enclosed by a hypersurface to a weighted total mean curvature of the hypersurface.

8 pages

Cited by in corpus (10)

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• A geometric inequality for convex free boundary hypersurfaces in the unit ball
• Inverse curvature flows in Riemannian warped products
• Inverse mean curvature flows in warped product manifolds
• Geometric inequalities involving three quantities in warped product manifolds
• On an inverse curvature flow in two-dimensional space forms
• Minkowski inequalities and constrained inverse curvature flows in warped spaces
• On the new weighted geometric inequalities near the sphere in space forms
• Alexandrov-Fenchel type inequalities with convex weight in space forms